2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67690We define a cotriple (co)homology of crossed modules with coefficients in a $π_1$-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with the (co)homology of the classifying space of a crossed module and with the cohomology of groups with operators. An example and an application are given.32 pages, LaTeX2e, Paul Taylor's diagram package; added reference. Accepted for publication by Homology, Homotopy and ApplicationsAlgebraic TopologyCategory Theory18G50; 18G30text